I read with amusement at the lukewarm posts about Taiwan in this forum.
As a Singaporean, and Singaporeans being Singaporeans, we LOVE Taipei. Most at least.
I suppose and maybe, you do need to speak Mandarin or even the local dialect Tai-yu to fully appreciate the charm of this country.
In fact, Taiwan should have its own board!!
1. Food
Like Japan, Taiwan with its highland and temperate climate, is land of agriculture and home grown produce. Do you know good Taiwanese rice, wasabi and maybe seafood are exported to Japan?
Have you tried the clean tasting Taiwan oysters?
This is from the famous Eel Shop, Fei Chian Wu. Skip the eel rice, slurp the oysters.
What about their famous Oyster Omelette? Top that on on their short grained rice... yummy!!
We are looking to take in Taiwan Kaiseki this coming week!!
2. Harajuku and Camden / Haji Lane
Taipei has its version of Tokyo's Harajuku, its near Zhongxiao Fuxing station, walk north, hit this whole area of shophouses, boutiques, cafes...
Between the Taipei Main Station and Zhongshan station, if you walk above, the whole area is like Singapore's Haji Lane or Camden in a way. Lotsa indie hipster shops, hairdressers, cult brands...
Spot arthouse film center and the MOCA are located here too. If things get too "boho" for you, step across the road and its HIGH STREET shopping!
3. Night Market, come on guys. Insiders go to SHIDA night market.
Why? This is near the university with a younger crowd and lotsa girls.

Of course there is the food. This is near Taipower station.
Right opposite, across the road is Rosevelt street, which is another indie area with the White Wabbit record shop where you can purchase Taiwanese indie music, post rock, ...